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Iman Setayesh

Publications and source records attributed to Iman Setayesh.

8 recordsLinked to original sources

An Event is Worth One Token: Event Tokenization for Industrial-scale LLM Recommendation

LLM-based recommendation has scaled along model capacity and sequence length, yet each position encodes only text, semantic IDs, or a few categorical features, discarding rich user, item, context, and outcome signals available at each event. Under autoregressive modeling, this yields weak queries at each position and, since each position becomes context for the next, the degradation compounds across the sequence. We propose an event-centric paradigm that represents each interaction by its full temporal snapshot, and identify a new scaling dimension we term snapshot resolution: the amount of information encoded per event. To efficiently scale snapshot resolution, we introduce AMBER (Autoregressive Modeling via Bottlenecked Event Representation), which compresses each temporal snapshot into a compact Event Token, a new LLM input modality. The representation is learned end-to-end, while Event Tokens are pre-computed and cached for serving, decoupling snapshot resolution from real-time serving compute. On industrial-scale ranking and retrieval benchmarks, AMBER advances the compute-quality Pareto frontier relative to alternative recommendation paradigms. At sufficient capacity, a single unified tokenizer even outperforms dedicated per-entity tokenizers, demonstrating positive transfer across structurally different entity types. AMBER's Event Tokens also transfer across model architectures: when integrated into a heavily optimized non-LLM ranker as serving-time historical features, they yield statistically significant improvements. Further scaling Event Tokenizer capacity provides additional improvements.

cs.IR

High $\ell$-torsion rank for class groups over function fields

We prove that in the function field setting, $\ell$-torsion in the class groups of quadratic fields can be arbitrarily large. In fact, we explicitly produce a family whose $\ell$-rank growth matches the growth in the setting of genus theory, which might be best possible. We do this by specifically focusing on the Artin-Schreir curves $y^2=x^q-x$.

math.NT

Combinatorial knot Floer homology and cyclic branched covers

Using a Heegaard diagram for the pullback of a knot $K \subset S^3$ in its cyclic branched cover $\Sigma_m(K)$ obtained from a grid diagram for $K$, we give a combinatorial proof for the invariance of the associated combinatorial knot Floer homology over $\mathbb{Z}$.

math.GT

On the kappa ring of $\overline{M}_{g,n}$

Let $\kappa_e(\overline{M}_{g,n})$ denote the kappa ring of $\overline{M}_{g,n}$ in codimension $e$. For $g,e\geq 0$ fixed, as the number $n$ of the markings grows large we show that the rank of $\kappa_e(\overline{M}_{g,n})$ is asymptotic to $$\frac{{n+e\choose e}{g+e\choose e}}{(e+1)!}\simeq \frac{{g+e\choose e}n^e}{e!(e+1)!}.$$ When $g\leq 2$ we show that a kappa class $\kappa$ is trivial if and only if the integral of $\kappa$ against all boundary strata is trivial. For $g=1$ we further show that the rank of $\kappa_{n-d}(\overline{M}_{1,n})$ is equal to $|P_1(d,n-d)|$, where $P_i(d,k)$ denotes the set of partitions $p=(p_1,...,p_\ell)$ of $d$ such that at most $k$ of the numbers $p_1,...,p_\ell$ are greater than $i$.

math.AG

On the structure of the kappa-ring

We obtain lower bounds on the rank of the kappa ring of the Delign-Mumford compactification of the moduli space of curves in different degrees. For this purpose, we introduce a quotient of the kappa ring, the combinatorial kappa ring, and show that the rank of this latter ring in degree $d$ is bounded below by $|P(d,3g-2+n-d)|$ where $P(d,r)$ denotes the set of partitions of the positive integer $d$ into at most $r$ parts. In codimension 1 (i.e. $d=3g-4+n$) we show that the rank of the kappa ring is equal to $n-1$ for $g=1$, and is equal to $\lceil \frac{(n+1)(g+1)}{2}\rceil-1$ for $g>1$. Furthermore, in codimension $e=3g-3+n-d$, the rank of the kappa ring (as $g$ and $e$ remain fixed and $n$ grows large) is asymptotic to $\frac{{n+e\choose e}{g+e\choose e}}{(e+1)!}$.

math.AG

Relative Hilbert Scheme of Points

Let $D$ be a smooth divisor on a non singular surface $S$. We compute Betti numbers of the relative Hilbert scheme of points of $S$ relative to $D$. In the case of $\PP^2$ and a line in it, we give an explicit set of generators and relations for the cohomology groups of this space.

math.AG